Question

which of the following equations is the most appropriate linear model for the data shown in the scatterplot?
a ( y = - 1.9 x - 10.2 )
b ( y = - 1.9 x + 10.2 )
c ( y = 1.9 x - 10.2 )
d ( y = 1.9 x + 10.2 )

Explanation:

Step1: Determine the slope sign

As \(x\) increases, \(y\) decreases. So the slope \(m\) is negative. Options C (\(y = 1.9x-10.2\)) and D (\(y=1.9x + 10.2\)) have positive slopes (\(m = 1.9>0\)), so we can eliminate C and D.

Step2: Determine the \(y\) - intercept sign

When \(x = 0\), from the scatter - plot, \(y\) is positive. The equation of a line is \(y=mx + b\), where \(b\) is the \(y\) - intercept. For option A (\(y=-1.9x-10.2\)), \(b=-10.2\) (negative). For option B (\(y=-1.9x + 10.2\)), \(b = 10.2\) (positive).

Answer:

B. \(y=-1.9x + 10.2\)